286 PHILlPS TECHNICAL REVIEW VOLUME 21

NUCLEAR MAGNETIC RESONANCE

by D. J. KROON. 539.143.42.082.722.56:620.18

The phenomenon of nuclear magnetic resonance in solids and liquids yields absorptionspectra from which val;'able information on their stTUctur~scan be obtained. The article belou;first gives a simple exposition of the theory, and then describes in more detail the equipmentrequired and a few applications. The latter illustrate the usefulness of the method both forpure scientific research and for routine investigations in various industries.

Introduction .

Amongst the most recent tools in the investigationof condensed phases (solids and liquids) are themethods of measurement that depend on the ab-sorption of electromagnetic energy at specific wave-lengths in the metre and centimetre regions. Accord-ing to the mechanism causing the absorption, themethods can be divided into three groups: para-magnetic resonance, nuclear magnetic resonance andcyclotron resonance.

In paramagnetic and nuclear magnetic resonancethe absorption is caused by the presence in thesubstance of elementary magnets, i.e. the "spins" ofelectrons and atomic nuclei which, in the presenceof a constant external magnetic field, are subjectedto an alternating magnetic field. Cyclotron resonanceoccurs when more or less free electrons (e.g. insemiconductors), in the presence of a constantexternal magnetic field, are subjected to an alter-nating electric field. In this article we shall beconcerned only with nuclear magnetic resonance.The related effect of paramagnetic resonance wasdescribed in an article published some time ago inthis journal I], to which we shall refer when occasionarises. An appendix to the present article deals insome detail with the points of difference betweenparamagnetic and nuclear magnetic resonance.

As mentioned, nuclear magnetic resonance occurswhen atomic nuclei exhibit a spin, that is to say,they have a net angular momentum and magneticmoment. This is so with many kinds of nuclei, inprinciple in all cases where the number of neutronsand the number of protons in the nucleus are notboth even. Familiar examples of nuclei that showa readily measurable effect, i.e. a marked absorption,are 19F, 23Na,27Aland 31p, but most especially IH,the hydrogen nucleus or proton.

The information that nuclear magnetic resonancecan provide is of various kinds. Hydrogen atoms arepresent in many inorganic solids (e.g. in molecules

1) J. S. van Wieringen, Paramagnetic resonance, Philips tech.Rev. 19, 301-313, 1957/58.

of water of crystallization) and in nearly all organicmolecules. The form in which the hydrogen nucleiare present has an influence on the resonancespectrum, i.e. the spectral distribution of themeasured absorption. In an organic liquid, forexample, each kind of molecule containing hydrogenshows a characteristic line spectrum, which cantherefore serve for identifying the molecule. In thisway it is possible to analyse mixtures of organiccompounds. Nuclear magnetic resonance equipmentis for this reason regularly used for routine analysesin the petroleum and oil-refining industries and theplastics industry. In solids the resonance frequencyof the H nucleus is very broad. From the spectraldistribution of the absorption here, one can drawconclusions regarding the ordering of H ions andother ions in the crystal and also regarding themotion of electrons and ions, diffusion phenomena,and so on.An earlier article in this Review explained how

nuclear magnetic resonance can also be used forthe accurate measurement of magnetic fields 2).Weshall touch on this application when describingthe equipment.In the following pages we shall first give a simple

theory of the phenomenon of nuclear magneticresonance. After describing the measuring equip-ment we shall consider, by way of illustration, someexamples of problems that have been studied by themethod of nuclear magnetic resonance. Whendealing with the equipment we shall distinguishbetween measurements on solids and on liquids.Owing to the different nature of their spectra, thesetwo states of aggregation call for different tech-niques of measurement.

For the determination of crystal structures the well-established methods of X-ray diffraction and infra-red ab-sorption can also be used. It is important to note, however,

2) H. G. Beljers, Three methods of measuring magnetic fields,Ill. Measurement by the proton-resonance method, Philipstech. Rev. 15, 55-62, 1953/54.

1959/60, No. 10 NUCLEAR MAGNETIC RESONANCE 287

that these methods are not so suitable when it is a matter ofdetecting and localizing hydrogen atoms.

X-ray diffraction depends on the scattering of X-rays bythe atoms or ions of which a crystal lattice is built up. Thisscattering decreases rapidly the lower the atomic number ofthe atom or ion. Scattering by H ions is so weak that informa-tion on these ions can be ohtained from X-ray-diffractionmeasurements only by indirect means. The related methodof neutron diffraction is better in this respect, and in facthas proved very useful 3). It can only he adopted, however,in laboratories associated with a suitable nuclear reactor.Moreover, in these investigations it is often desirable to replacethe hydrogen ions (protons) by ions of heavy hydrogen(deuterons), which of course is only practicable in specialcases 4).

The infra-red absorption of hydrogen atoms bound tooxygen (OH vibrations) is readily measurable. The frequencyof these vibrations depends markedly on the surroundings ofthe OH group in the lattice, and it is frequently possible todeduce the configurations in which the OH group occurs inthe crystal. The interpretation of the measurements, however,is very complicated and the information obtained is generallyinsufficient for a complete determination of the structure.Furthermore, the sample under measurement is required tobe transparent to some extent, which often calls for the useof special techniques.

The method of nuclear magnetic resonance is thus a usefulcomplement to the older methods of structure determination

Historical note

Äs long ago as 1936 the Dutch physi eist C. JGorter predicted the possibility that electromag-netic waves would be absorbed in a solid through theagency of the atomic nuclei if these were subjectedto an external magnetic field. His experiments at thetime produced no results. It later appeared that thesubstances on which the experiments were donehappened to show only a very small effect, and thiswas the main reason for the failure of the experi-ment. Some years later, thanks to the advances inhigh-frequency techniques, the physicists F. Blochand E. M. Purcell, working independently and withdifferent methods of measurement, were able toconfirm Gorter's theory. In 1952 both these Ameri-can workers were awarded the Nobel prize forphysics.

Concise formulation of the theory of nuclear magneticresonance

In general an atomic nucleus possesses, apart frommass and electric charge, an angular momentum anda magnetic moment. In the classical model, theatomic nucleus is imagined to behave like a rapidly

3) G. E. Bacon, Neutron diffraction, Oxford Univ. Press,London 1955. See also G. E. Bacon, Ned. T. Natuurk. 25,5, 1959 (No. I).

4) G. R. Ringo, Neutron diffraction and interference, Section36, Handb. Physik, VoL32, Springer, Berlin 1957, p. 603.J. A. Goedkoop and B. O. Loopstra, Ned. T. Natuurk. 25,29, 1959 (No. 2).

spinning magnetic top, the magnetization being inthe direction of the axis of rotation. Quantum-mechanical considerations require that if the nucleusbe subjected to a constant external magnetic field,the axis of rotation of the top, which precesses aboutthe field direction, can assume only certain discreteorientations with respect to the direction of themagnetic field. The number of possible orientationsdepends on the magnitude of the angular momen-tum. For hydrogen nuclei (protons) there are twopossible orientations, viz. in the direction of the fieldand opposite thereto. Other nuclei have two or morepossible orientations (fluorine 2, sodium 4, bismuth10).

The energy of the nuclear magnet in the magneticfield is:

E = flB cos {},

where fl is the magnitude of the magnetic moment,B the field strength (induction) and {} the anglebetween the elementary magnet and the externalfield (fig. I). The possible values of cos fj. are givenby the formula:

mIcos {}= ~====

iI(1 + 1)

B

99721

Fig. 1. Magnetic dipole (moment ft) in a magnetic field B.

where J, the spin quantum number of the nucleus,is a multiple of t, and mI can assume a number(21+1) of discrete values, each differing by 1, theextremes being 1and -J. The energy E can alsobe written in the form:

mIE = flzB ['

where flz = fll!1/(1 + 1) represents the largestpossible projection of fl on the axis of the field,The magnetic moment fl is given by:

fl = g i1(J + 1) ...!...!!_,4nmp

(1)

where e and mp represent respectively the chargeand mass of the proton, and g is a numerical constant

~~----~_.~--------------------------------------------------~--------------------------------------------

288 PHILIPS TECHNICAL REVIEW VOLUME 21

that differs according to the type of nucleus (ingeneral g is between 0.1 and 10).The spin quantum number for hydrogen nuclei isI = t. There are thus, as remarked, only two statespossible. The energy difference between these statesis

In an external :field B = D.5 Wb/m2 [5000 gauss]this energy difference is of the order of 10~26 J(10-7 electronvolt).If the nucleus is subjected simultaneously to a

constant magnetic :fieldand an alternating magnetic:field at right angles thereto, there is a possibilitythat the atomic nucleus will change from the onestate to the other, whereby an amount of energyequal to the difference L1E will be absorbed from thealternating :field or given up to it. The condition forthe occurrence of such transitions is that the fre-quency J of the alternating :field should satisfy:

L1EJ=-,h

where h is Planck's constant (h = 6.62 X 10-34 Js).Eliminating L1E from the expressions (2) and (3)

gives the condition for resonance absorption as

or, after substitution of Il:; (from (1)) and putting1= t:

eJ=g-.--B.4.:n;mp

For hydrogen nuclei flz is 1.4 X 10~2GA.m2. In a :fieldof B = 0.5 Wb/m2, as mentioned above, we thushave J= 21.3 Mc/s.

The procedure for observing the absorption isbasically as follows. A sample of the substance havingsufficient nuclei of the type under investigation isintroduced into a coil which is connected to a weakhigh-frequency source of roughly the resonancefrequency Jo. The coil is placed between the poles ofa magnet and the magnetic :field is slowly varied.When the magnetic field Bo reaches the value givenby (4.a)-- for the frequency Jo -- resonance occurs,giving rise to a slight energy absorption whichresults in a change in the Q of the coil. By includingthe latter in a suitable circuit, e.g. a bridge circuit,the change in the Q can be measured and recordedas a function of B, to give the magnetic absorptionspectrum. The effect of relaxation phenomena onthe absorption will he touched on presently.

(2)

Structure of the absorption spectrum

From' the mechanism described it might beinferred that resonance absorption occurs only at asingle frequency, determined by (4a) or, if thefrequency Jo is given, at a certain induction Bo,given by:

The experiment shows; however, that absorptionoccurs in a certain region of B values around Bo,and that the recorded absorption line thus has acertain width, and sometimes a certain stru~ture.This may partly be attributed to the fact that,whereas a field B has been applied and measured,the nuclei investigated may in reality be in a :fieldthat differs from B by a small amount b. Theresonance condition is then:

(3) orB = Bo-b.

(4a)

Absorption thus occurs at a value B of the meas-uring :field that differs from Bo. If b differs forvarious parts of the specimen or for various kindsof nucleus, the result is a broadened line or a linespectrum. One mayalso conceive of performing theexperiment such that the external :field (Bo) is keptconstant and the frequency J varied. In thatcase resonance would occur when J = Jo + L1J=(2flz/h)(Bo + b), so that L1J= (2flz/h)b. The valueL1J= 1 cis corresponds to b = 2 X 10~8 Wb/m2.

Various reasons can be given for the occurrence ofthe :field-strength deviations b. The first is quitetrivial, being of an instrumental nature and con-nected with the fact that the magnetic field is notperfectly uniform. As a result, parts of the specimenare found in a :field that is not exactly identicalwith the field B. This source of broadening canhe reduced to negligible proportions by using smallspecimens and a magnet whose air gap is narrowcompared with the diameter of the pole pieces. Thisapplies at least to solids in which, for other reasons(to be discussed), marked broadening effects occurin any case. In liquids, which generally exhibit aspectrum having sharp resonance lines, the instru-mental broadening may not be negligible.

Another cause of instrumental broadening isfound especially when recording the spectra ofsolids. As we shall see, in such cases the measure-ment is performed by :finding an average value overa range oB of field strengths. Since oB cannot be

(4b)

1959j6Q, No. 10 NUCLEAR MAGNETIC RESONANCE 289

made infinitely small, this also gives rise to linebroadening (see later, fig. lOa).

The other causes of line broadening and of theoccurrence ofline spectra, discussed in the following,are essentially concerned with the physical condi-tions to which the nuclei are subject during theexperiment, and about which the absorption spec-trum can therefore provide information.

Local fields in crystals

For the present we shall confine the discussion tosolids, that is to crystals. In a crystal the field actingon the nuclei consists of the external field B (nowassumed to be uniform) together with the dipolefields of neighbouring nuclei. For hydrogen nucleithis dipole field at a distance of 1 A is of the orderof 10-3 Wb/m2. The total field acting on a nucleussubjected to a dipole field b is B + b. At resonancewe again have B + b = Bo, hence:

B = Bo - b.

The resonance line is then (in terms of B) displacedover a distance b,A case frequently encountered is that of two

neighbouring protons. This is found when investi-gating the absorption of two protons of a moleculeof water of crystallization (H-O-H). The field bcaused by the one proton at the position of the otherdepends on the distance r between the two protonsand on the angle fi which the line connecting themmakes with the external field B. The dipole field isgiven by:

ftzb = ± - (3 cosê fl- 1).

r3

The ± sign arises because the "perturbing" protoncan be oriented in two ways in the field B. For onepair of protons we then obtain, instead of a singleresonance peak, two peaks at a distance 2b apart.We shall see presently that, as regards the magni-tude of the effect, this statement requires somemodification.This, then, is the situation when we have a single

crystal and consider the proton pairs therein whichtake up a specific orientation with respect to thecrystal axes. If we turn from a single crystal to apowder, we find that the angle fl for the kind ofproton pairs considered has a different value ineach crystallite of the powder. The resonance pat-tern is consequently smeared out to a broad band inwhich, however, two peaks can still he recognized.

So far our discussion has taken account only ofneighbouring protons forming a particular H-H pair,for example the protons of a single H-O-H molecule.

These protons will also, however, he subjected to thedipole fields of protons of other H-O-H moleculesand in addition to the dipole fields of other crystalnuclei. This causes a further broadening of the ab-sorption pattern. As an example .fig. 2 shows theproton-resonance absorption of a powdered speci-men of potassium fluoride (KF.2H20).

11 I1

It "I1 "" nI I'\ ,I 'I I\ I\ 1\ 1

\, ~/......__ ....

-LIB 99722

Fig. 2. Spectrum of the absorption caused by proton resonancein a powder sample of potassium fluoride (KF.2H20).The dashed line represents the theoretical shape of the

spectrum if there were only interaction between the protons ofa single molecule of water. For calculating this curve thedistance between the peaks was taken as 11X10-4Wbfm2, andthe area below the curve was made equal to that under theexperimental curve.

(5)

In the simple case of isolated proton pairs it is afairly simple matter to predict a theoretical absorp-tion curve that compares reasonably with the ex-perimental result. In more complicated cases this isnot so easy. In such cases, only the "second mo-ment" of the broadened line is determined. If theline shape is given by

y = f(B),

its second moment is given by

(LlB)2 = feB - Bo)2y dB/fY dB.

If the value of (LlB) 2 has been found experimentally,it can be compared with the theoretical value, forwhich Van Vleck derived the following 5):

Here rjk represents the distance of a perturbingproton (j) to the perturbed proton (k), fljk the anglewhich the vector r makes with the external field, andC a constant comprising, among other things, themagnetic moments of the nuclei. The summationshould really he extended over all the protons of the

5) J. H. van VIeck, Phys, Rev. 74,1168,1948.

290 PHILIPS TECHNICAL REVIEW VOLU_ME21

crystal, but in practice it is sufficient to take only asmall volume element of about 10Á diameter.

Let us now return for a moment to the magnitudeof the broadening. Apart from the "static" mutualinteraction of the ions, referred to above, there isalso a dynamic interaction, resulting from the factthat the protons, owing to their precession about thedirection of the field, generate local alternating fieldsas well as a local static field. It would be going toofar to deal with the complete quantum-mechanicaltreatment of this problem, which takes into accountboth the static and the dynamic effects 6). The result,however, is fairly simple, and states that the ex-pression (3 cos'' f) - 1) occurring in the formula mustbe multiplied by a factor of -fr, making the totalbroadening 1times the static broadening.

Ifwe consider only two protons, we see that they can orientthemselves in three wayswith respect to the field: both parallel,one parallel and the other anti-parallel, and both anti-parallel.This gives rise to three energy levels each being LIE = 2p.Bapart (see formula 2).The mutual interaction described above (analogous to two

coupled pendulums) perturbs the energy levels. As a result,the separation of the energy levels is now:

This means that resonance is found for

B = Bo ± 1-pr3 (3 cos" f} - 1), . . . . (6)

which, except for the factor -\1-, is the same as (5). Thc factor ïdoes not occur in the broadening caused by the influence ofother nuclei on the protons, for which the static calculationgives the correct result.

Interaction with the crystal lattice

Apart from the interaction between the protonsmutually and between the protons and other nuclei,interactions occur between the protons and theatoms of the specimen as a whole. This too gives riseto additionalline broadening.

This additional broadening can be explained withthe aid of Heisenberg's uncertainty principle. Thistells us that the energy LIE of an excited state isindeterminate by an amount oE, given by:

oE Ot l'O:::i h.

The quantity & in the present case is a "relaxationtime" -r, the significance ofwhich is as follows. In theabsence of an external field the spin directions arerandomly distributed owing to thermal equilibrium.If, at a given moment, all spins were made parallel,then as a result of interaction with the lattice this

6) See, for example, E. R. Andrew, Nuclear magnetic reso-nance, Cambridge Univ. Press, London 1955, pp. 152-154,240-242.

ordering would relax and ultimately vanish accord-ing to an exponential law:

In the case of protons in a liquid -r is of the order of10 sec and therefore -r-l"= 0.1 cjs. With the aid of(7) we find that this corresponds to an additionalbroadening of approximately 2 X 10-9 Wbjm2. Insolids -r may have a wide range of values, but theadditional broadening here is I almost invariablynegligible compared with the other causes of linebroadening.

Thus, although the interaction with the lattice orwith the environment is often negligible as regardsthe effect on the line width, it is really essential tothe occurrence of resonance absorption. In an exter-nal field B in which there are N protons, the numberof parallel-aligned protons (NI' state 1) at thermalequilibrium is greater than the number of anti-parallel-aligned protons (N2, state 2), to an extentgiven by:

exp (- LJEjkT), (8)

where T is the temperature and k is Boltzmann'sconstant (k = 1.38X 10-23JrK). If, now, an alter-nating field of the desired frequency is applied, andif there were no interaction with the lattice, aftersome time a state would arise where NI = N2 = tNoFrom that moment onwards as many protons wouldgo over per unit time from state 1 to state 2 as fromstate 2 to state 1, and no absorption would be ob-served. The interaction with the lattice, however,tries to restore the situation (8); consequently, evenwhen an alternating field is present, NI remainsgreater than N2, and absorption can, therefore, stillbe observed. Also, it follows from this that, for thepurpose of detecting the absorption, the alternatingfield should not be too strong. These points werealready discussed in connection with paramagneticresonance in the article quoted under 1).

(7)

Structure of the spectrum in liquids

In contrast to crystals, where the line widths maycover 10-4 to 10-2 Wbjm2, the resonance lines foundfor liquids are very narrow, of the order of, e.g.,10-7 Wbjm2. Special measures, to be discussed later,are therefore necessary to keep the instrumentalwidth (non-uniform field) below this limit. The factthat the marked line broadening found in crystalsdoes not occur in liquids is due to Brownian motionwhich, in classical terms, so frequently perturbs thephase of the precessional movement that only theeffect of the average field remains, the action of

1959/60, No. 10 NUCLEAR :l\iAGNETIC RESONANCE 291

neighbouring fields being eliminated by averagingwith respect to time. The interaction with the me-dium remains as the sole cause of line broadening.As in crystals, however, this is a very slight effect.

The result of this situation is that, at fieldstrengths of, say, 10-5 Wb/m2, displacements andsplittings of a resonance line are observed which aredue to effects that mayalso be present in the solidbut escape observation because of the large totalbroadening in the case of solids. These effects arelargely attributable to the action of the magneticfields of electrons. It is due to them that the spectraof various organic compounds differ so markedlyfrom one another and can even be used for identi-fying these compounds. Weshall deal with thissubject at greater length when discussing the practi-cal examples.

Equipment for nuclear-magnetic-l'esonance investi-gations

Investigations on liquids

As remarked, for observing nuclear magneticabsorption in liquids the magnetic field should behighly uniform. The field variation over the dimen-sions of the specimen (a few millimetres) should beless than 1 : 106•

To obtain a' sufficiently -uniform magnetic fieldfor these kinds of experiment, magnets are used, asmentioned above, in which the air gap is narrowcompared to the diameter of the poles of the magnet.The pole pieces should be made of highly homogene-ous material and ground optically flat. The remain-ing non-uniformity of the field is corrected by pass-ing a current through suitably-positioned flat coilson the pole faces.With the object of achieving a still higher resolu-

tion, the specimen is often rapidly rotated. This hasa narrowing effect sim,ular to that discussed aboveas regards the influence of the Brownian motion onthe internal fields: the differences in macroscopiefield strength are eliminated by averaging withrespect to time. In this way a resolution of 10-8Wb/m2 can be achieved.During the measurement the magnetic field

should remain constant. In the case of an electro-magnet, a highly stabilized current should be used,constant to within 10-6 of the desired value.Residual, relatively small fluctuations due to othersources are compensated by means of a coil of manyturns wound round the magnet poles. The e.m.f.induced in this coil by a flüëtuating magnetic fieldis amplified and converted into a current which is

fed in anti-phase to a correction coil on the magnet.In this way a constancy of 3 in 108 can bemaintained for several minutes.

An easier method to attain constant magneticfields is to use a permanent magnet. The onlyimportant cause of deviations of the magnetic fieldin this case is that the magnetization of the magneticmaterial (e.g. "Ticonal") is temperature-dependent,The temperature of the magnet should change by nomore than 10-4 oe if a constancy of 1 in 108 is to beattained. The magnet is therefore placed in athermostat. Owing, to, the high thermal capacityof the magnet, a simple thermostat is sufficientto cope with the fluctuations of the ambient tem-perature.

The frequency of the applied alternating field, too,should have a stability of 1 in 108• This can beobtained by using a crystal-controlled oscillatorplaced in a thermostat. If a number of such crystalsare available, various kinds of nuclei can be investi-gated. Since, however, as mentioned, nuclear mag-netic resonance is mainly used for the investigationof organic compounds, the resonance of protons isof primary interest.The variation of the magnetic field required for

scanning the spectrum is produced by means of anadditional excitation coil, through which a currentis passed that rises very slowly and linearly fromzero to a maximum (sawtooth waveform). In thecase of a liquid spectrometer the maximum value ofthe field variation need only be quite small (a few10-4 Wb/m2).Various types of high-resolution spectrometers are

described in the literature, and some are also com-mercially available. As an example we shall mentionsome particulars of the high-resolution spectrometermarketed by Mullard (type SL 44 M02). This usesa permanent magnet which is accurately maintainedat a constant temperatrrre. The magnet gives a fieldof 0.9 Wb/m2 and has poles of 15 cm diameter and agap 3 cm in length. The resonance détector consistsof a double-T measuring bridge, which is connectedto a high-frequency amplifier, followed by a diodedetector. The output voltage of this detector, whichis proportional to the output voltage of the bridge,is applied to an oscilloscope having a long-persistencescreen and to a recording unit. The bridge is fedby a crystal-controlled oscillator of 40 Mc/s. Thespecimen holder consists of a glass tube of 3 mmdiameter, which is fillêd with the substance forinvestigation and rapidly rotated. The photographin fig. 3 gives an impression of the equipment. Ablock diagram appears in fig. 4; some additionaldetails are given in the caption.

292 PHILIPS TECHNICAL REVIEW VOLUME 21

9965~

Fig. 3. Mullard equipment for nuclear-magnetic-resonance investigations on liquids (high-resolution spectrometer, type SL 4·4.M02).

Investigations on solidsSince the width of the lines in solids is generally

very large (10-4 to 10-2 Wb/m2), a highly uniformfield is not necessary for absorption measurementson solids, nor need the field be so highly constantwith time or the measuring frequency so stable.

On the othcr hand the absorption at a given fieldstrength is now roughly a hundred times weaker.Compared with liquids, therefore, larger specimensare used and more sensitive equipment. The highersensitivity is achieved by a different measuringprocedure (see below). Higher demands are alsomade on the versatility of the spectrometer, since insolid-state investigations it may be necessary tomeasure the resonance of a large number of elementsthat may occur in crystals. Whilst the study ofprotons is often important for the determination ofcrystal structures (water of crystallization), theresonance of other nuclei (Cu, AI, etc.) enters intothe study of metals. Investigation of the structure ofthe resonance line as a function of temperature, forexample, makes possible the study of a number ofeffects (such as atom movements, which make theresonance line narrower, and diffusion phenomena).

As an example of a solid-state spectrometer weshall discuss the equipment used in the Philips

Research Laboratories at Eindhoven. A block dia-gram of the set-up is shown in fig. 5.

99723

Fig. 4. Block diagram of the Mullard spectrometer in fig. 3used for liquid analysis. Magn permanent magnet (induetionin air gap 0.9 Wb/m"). L alternating-field coil in which thesample is placed. 0 crystal oscillator, fr~quency 40 Mc/s, forgenerating the high-frequency alternating magnetic field insidethe coil L. B measuring bridge. A preamplifier. R receiver.G diode detector. K cathode-ray oscilloscope. Reg recorder.Var generator of auxiliary current for the sawtooth variationof the static magnetic field used for scanning the spectrum.The current source Sh is used for correcting the magnetic fieldin the air gap to match it to the oscillating frequency of thecrystal.

1959/60, No. 10 NUCLEAR MAGNETIC RESONANCE

The field for this spectrometer is again generatedby a permanent magnet. The fairly considerablerange of field strengths required for the analysisof solids is obtained here by means of gaps of

shows what happens. A portion of the resonance lineof width oB is scanned. The resultant signal, whenoB is sufficiently small, is proportional to thederivative dy/dB of the absorption curve y = f(B).

,L

~ ~Oh.~

.____ K Kcal f- l-A

'--

n n

\. Cr)r- e--

~°mod ~ n~

..~~

I-

Magn~ -

~y Serv~

~ \ L~L.- ecal -

u

IF

Ir J 0 0I °calI

99724Fig. 5. Simplified'block diagram of the solid-state spectrometer in Eindhoven. Magn per-manent magnet (induction in air gap 0.45 Wb/m2). Mot synchronous motor with gearboxfor shifting the yoke bars of the magnet, thereby effecting a continuous change of the fieldin the air gap (spectrum scanning). Cr cryostat, containing alternating-field coil and sample.Oh oscillator for generating the high-frequency alternating magnetic field in this coil.Lmod coils for the low-frequency modulation of the static magnetic field, fed by the oscil-lator Omod (230 cis). A selective amplifier. K cathode-ray oscilloscope for observing theoutput signalof Oh. Reg recorder. LcRI calibrating coil, used in conjunetion with oscillatorOenl for calibrating the magnetic field by means of proton resonance. Serv servo amplifier,which keeps the calibrating oscillator tuned to proton resonance; this ean be checked onthe oscilloscope Kcnl. J crystal-controlled oscillator with mixer stage, supplying thecalibration pulses to the recording apparatus. F frequency meter.

variable length in the yoke. With the aid of a camthe yoke bars can be raised, thereby decreasing themagnetic field. A particular advantage of this con-struction is that, within a certain range, the fieldcan be reproducibly adjusted to any desired value,so that no auxiliary field is needed for matching tothe oscillator frequency (cf. Sh in fig. 4).The cam is driven by a synchronous motor via a

gearbox, enabling the spectrum to be continuouslyscanned. The shape of the cams is such as to ensurethe most linear possible variation of the field withtime. As in the case of a high-resolution spectro-meter, this is desirable in order that equal distanceson the uniformly moving strip chart in the recorderwill correspond to equal variations of B.To the slow field variation a low-frequency sin-

usoidal modulation of very small amplitude is added(coils Lmod and oscillator Omod in fig. 5). Fig. 6

y =f(B)

r ---lIlIill-t

-8

99725

Fig. 6. Illustrating the scanning of a broad line by a low-fre-quency alternating magnetic field. The result, the derivativedy/dB of the absorption y = f(B), is recorded. oB = modu-lation width, S = resultant signal.

293

294 PHILIPS TECHNICAL REVIEW VOLUME 21

This method of measurement has the advantageover the simpler method used for liquids' that ampli-fication is now possible in a very narrow bandaround the modulation frequency (230 cJs). As aresult the unavoidable noise from the amplifier issuppressed and a considerable gain is achieved inthe signal-to-noise ratio.

This method cannot be used with th( liquid spectrometerbecause the line width, expressed in terms of frequency, is sovery small (0.1 cIs). Modulation with a practical frequency,which-must be at least thirty- or forty CIS, would give rise toundesh:able line broadening and satellite lines. However, sincethe absorption intensity in liquids is so much greater, a lowersensitivity is sufficient in their case.

The signal is detected, in the present equipment,with the aid of the same oscillator 7) that suppliesthe high-frequency voltage to the alternating-fieldcoil. This is done by making the coil form part of thefrequency-determining network of the oscillator. Asmall change in the properties of the coil (the Qchanges depending on the absorption of the speci-men inside it) causes a considerable change in thevoltage of the oscillator.

After detection the low-frequency signal is ampli-fied in a narrow-band amplifier (A in fig. 5) andmixed with an alternating voltage whose frequencyis equal to the modulation frequency. This finallyproduces a D.C. voltage which is proportional to thederivative of the resonance peak and is recorded ona strip chart. Examples of such recordings appear infig. 10.A second specimen and coil are present in the

magnetic field. By means of proton resonance in this(liquid) specimen the magnetic field is continuouslymeasured and calibrated by comparison with thesignal from a crystal-corrtrolled oscillator (J in fig.5). The calibration marks appear on the recording.In the present equipment the distance between themarks is 1.17xl0-4 WbJm2• This again clearlydemonstrates the difference between the spectra ofliquids and solids. Broadly speaking, about 20calibration marks appear on one spectralline in thecase of solids, whereas there may be 20 completeliquid spectra between two such calibration marks.

For measurements at low temperatures the com-plete specimen holder can be placed in a cryostat.With the set-up now in use, measurements can bemade at temperatures as low as 20 OK; the recentavailability of liquid He now makes it possible tomeasure down to 1.2 OK.'

7) H. A. Thomas, Electronics 25, January 1952, p. 114.

The caption to fig. 5 gives further particulars ofthe equipment. The photograph in fig. 7 gives animpression of the set-up. The permanent magnet isshown separately in fig. 8, showing the mechanismfor varying the air gap.

In the adjoining table some properties of the twonuclear magnetic spectrometers discussed are setout side by side.

High-resolution

spectrometerSolid-statespectrometer

Specimen size 10 mmê 1000 mm''Non-uniformity of the magneticfield over the whole of thespecimen 1: 106 1: 5 X104

Instability of the static mag-netic field with time 1: 108 1: 105Instability of the alternatingfield 1: 108 1: 105Resolving power LIBI B 1: 2xl07 1: 5 X104

rHSuitable for the nuclei: especially 1°F numerous3lp

Modulation of static magneticfield sawtooth sawtooth +

low-freq.sine wave

Amplitude of sawtooth 0.0002Wbfm2 0.03 Wbfm2

Recorded quantities absorption dy/dBy = f(B)

Measurement at low tempera-tures no yes

There now follow some simple examples of thepractical application of nuclear magnetic resonance.

Examples

The spectrum of ethyl alcohol

The ethyl-alcohol spectrum reproduced in fig. 9was recorded with a Mullard spectrometer. Thespectrum consists of a number of very fine lines, andits total width is only 5X10-6 WbJm2• Since it is thespectrum of a liquid, the marked broadening usuallyfound in solid spectra is lacking. The lines are due tohydrogen nuclei in the sample.

Let us now examine the structure of the spectrum.more closely. There are three groups of lines. Theintegrated areas of each of the three groups arefound to be in the ratio 3 : 2 : 1, corresponding to theform.ula CHa-CH2-OH. Why have these three groupsa slightly different frequency and why is each groupsplit into components (viz. 3, 4 and I)?

The magnetic field at.the position of one of theprotons of the molecule is composed of the externallyapplied field plus the field produced by the surround-

1959/60, No. 10 NUCLEAR MAGNETIC RESONANCE 295

Fig. 7. Apparatus for the study of nuclear magnetic resonance in solids, in use at thePhilips Research Laboratories, Eindhoven.

ing valency electrons. The electron density in themolecule is lowest in the OH group and highest inthe CH3 group, and for this reason the electron fielddiffers for the three groups that make up the mole-cule. This causes the splitting into three groups oflines.

The splitting into components of a single group oflines arises as follows. The electrons move throughthe entire molecule and, as it were, communicateinformation to the nuclei regarding their immediateenvironment. Since, for example, the protons of theCH2 group can assume different orientations inrelation to the external field, the electron orbits canbe polarized in different ways by the spin field ofthese protons. This gives rise to a change, albeit avery small one, in the magnetic field which the elec-trons produce at the position of the neighbouringgroups. The two protons of the CH2 group mayeither be both parallel with the measuring field, orone may be parallel and the other anti-parallel, orboth anti-parallel. The total magnetic moment of

Fig. 8. The permanent magnet in the solid-state spectrometerat Eindhoven. On the right-hand side can be seen the toothedsegment which is slowly turned by the motor via a gearbox(extreme right); attached to the segment is a cam which pnshesthe four radially mounted pins outwards. These raise slightlythe four yoke bars, two of which can be seen in the photograph,thereby lengthening the total air gap in the magnetic circuit.This produces the desired time-linear variation of the magneticfield in which the sample is situated.

296 PIIILlPS TECHNICAL REVIEW VOLUME 21

99692

Fig.9. Spectrum of ethyl alcohol (CH3-CR2-OH), recorded with the Mullard spectrometer(fig. 3). In the spectrometer used, the magnetic field was 0.75 Wh/m2.

the CH2 group is then respectively 2flz, zero or-2flz. The probabilities of these three cases occurringare in the ratio of 1 : 2 : 1. This causes the linebelonging to the protons of the CH3 group to be splitinto three components with an intensity ratio of1 : 2 : 1. In the same way we can argue that the linepertaining to the protons of the CH2 group is split,under the influencc of the neighbouring CH3, intofour components with an intensity ratio of 1 : 3 : 3 : 1.

Special considerations apply to the line due to theOH group. One might expect that this line, undcrthe influence of the neighbouring CH2 group, wouldalso be split into three components of intensityratio 1: 2 : 1. Only one line, however, is in factfound. The explanation is that the alcohol sampleused contains impurities in the form of traces ofwater, acid or base. Since the electron densityaround the OH group is small, the proton of theOH group can easily break away. Where traces ofimpurity are present there is therefore a constantexchange bei.,w~ell the H ion af the OH grO!lp a nrl

the H ions of the impurity. This proton exchangeoccurs for every molecule very many times persecond. The time during which a proton of theOH group is under the influence of the polarizedelectron orbits in the alcohol molecule is thereforeextremely short, and the average frequency of theexchange is high compared with the frequencydifference between the splitting components of theline group, which would exist if there were no suchexchange (approx. 10 cis). As a result there is noeffective splitting into components. In extremelypure alcohol the line of the OH group does show theexpected splitting into three components.

The further details visible in the spectrum are dueto second-order effects which do not enter into thescope of this simple explanation and will not bediscussed.It should be noted that the described spin-spin

interaction, via the polarization of the electronorbits, differs essentially from the direct spin-spininteraction which occurs in solids and which, in ourcase, is made ineffective by the Brownian motion ofthe molecules.The above inferences drawn from the nuclear

magnetic resonance spectrum are an elegant con-firmation of the structure of the alcohol molecule,already determined by other means. It is evidentthat in other cases valuable information can beobtained from liquid spectra, that can serve fordetermining an unknown structure.The other examples to be discussed refer to solids.

They concern investigations made, or still inprogress, in Philips Research Laboratories at Eind-hoven, and in all cases involve proton resonance.

Hardening of +Araldite"

The hardening of "Araldite" (Ciba, Basle) is astriking example of the transition of a fluid into thesolid state. Araldite is a widely used syntheticadhesive of the epoxy-resin type. The adhesiveconsists of two fluid components, the epoxy resinand a hardening agent added and mixed just beforeuse. After about 30 hours the adhesive has set hardas a result of polymerization of the epoxy molecules.Some spectra, recorded at various times during thehardening process, are shown in figs. lOa, band c.It can be seen how the original very narrow liquid

1959/60, No. 10 NUCLEAR MAGNETIC RESONANCE 297

line, whose width is determined by instrumentalcauses, develops into a solid-state line having awidth of about 2 X 10-3 Wb/m2• The variation of thesecond moment with time indicates that the linebroadening takes place in several more or lessdistinct stages. This allows inferences to be drawnregarding the gradual slowing-down of the motionsof various groups of atoms in the molecule. Thissubject has been studied more extensively byLösche 8).

Motion of hydrogen gas in metals 9)

The following example refers to the motion ofhydrogen gas in metals. Some metals and alloys canabsorb relatively large amounts of gas, e.g. hydrogen,and for this reason they can be used as getters inradio valves. One of these alloys is thorium-alumi-nium, Th2Al. The crystal structure of this alloy hasbeen extensively studied 10), and it is found that a

8) A. Lösche, Arch. Sciences 10, fase. spéc., p. 197,1957.9) D. J. Kroon, C. van de Stolpe and .J. H. N. van Vucht,

Arch. Sciences 12, fase. spéc., p. 156, 1959.10) P. B. Braun and .J. H. N. van Vucht, Acta cryst. 8, 24,6,

1955.

Fig. 10. Recordings of the derivative of the absorption of "Araldite" during hardening.a) Ten minutes after mixing. The width of the line is determined by the modulationwidth öB. b) Seven hours after mixing. The foot of the curve already shows some broad-ening. c) Twelve hours after mixing. The curve shows marked broadening.

The recordings were made with arbitrarily decreasing or increasing magnetic field;in (a) and (b) the field happened to be increasing, in (c) decreasing.

a b

maximum of four atoms of hydrogen is taken up permolecule of Th2Al. Between the metal atoms are twointerstices, each of which can entrap two H atoms.We shall consider the compound Th2AIH2, in whichhalf the number of available interstices are filled.

At room temperature a very narrow resonance linewas found with this compound. Partly from theintensity distribution in the line it was concludedthat this narrow line is due to protons that jumpvery rapidly from one interstice to a neighbouringunoccupied one. Owing to this movement the dipole-dipole interaction between neighbouring protons isaveraged out. At low temperatures (T < 100 OK)a line width of 8 X 10-4 Wb/m2 was found. Since8 X 10-4 Wb/m2 corresponds to a frequency differ-ence of about 4,X 104 cis, it may be inferred fromthis that under these circumstances the time spentby a proton in an interstice is long in relation to3 X 10-5 sec. Measurement of the line width as afunction of T produced the curve shown in jig. 11.From the temperature at which the line-narrowingbegins, in conjunction with the value of the linewidth at low temperature, it is easy to determinethe way in which the average jump frequency 1's

c

298 PHILlPS TECHNICAL REVIEW VOLUME 21

depends on the temperature. With a minor simpli-fication this can be described by the formul~:

'Vsa: exp (-Ea/kT),

where Ea represents the activation energy of the dif-fusion process. This is found to be equal to 0.22 eV.From the intensity distribution of the absorptionline it can be inferred that at low temperature short-range ordering of the protons exists. This investiga-tion is being pursued.

.tJB

t8

\7

6 \5. 1\

\\

2 \1

\-=

/,H

4

3

o200 250

-T3CXJOK99726

/00 /50

Fig. 11. Line width of the resonance in Th2AIH2 as a functionof temperature.

Positions of protons in aluminium hydroxides 11)

To illustrate the application of the second-moment determination discussed above, we shallconsider an investigation of aluminium hydroxide.Various hydroxides of Al are known, each with itsown crystal structure; examples are hydrargillite(y-AI(OH)a), bayerite (a-AI(OH)3) and boehmite(y-AlOOH). We shall deal here with the firstcompound mentioned. The 0 atoms in this com-pound form a triangular layer structure. There areseveral conceivable sites for the H atoms; two arerepresented in fig. 12a and b. The theoretical valueof the second moment (with an O-H distance of0.96 Á) is 26 X 10-8 (Wb/m2)2 in the case a, and29.4 X 10-8 (Wb/m2)2 in the case b. The value foundby experiment is (26.5 ± 1.2)X10-8 (Wb/m2)2,which argues in favour of the first assumption.Other crystal models that have been proposed givea widely different value, e.g. 15X10-8 (Wb/m2)2,and must therefore be rejected.

Finally, it may be noted that the few, verysimplified examples of applications discussed here

11) D. J. Kroon and C. van de Stolpe, Nature 183, 944, 4thApril 1959.

are by no means representative of all the possibilitiesoffered by nuclear magnetic resonance, A list of thepublications that have appeared so far on thesubject of nuclear magnetic resonance would takeup just as many pages as this article.

b 99727

Fig. 12. In a crystal of y-AI(OH)alayers of Al atoms alternatewith double layers of 0 atoms. In the figure the 0 atoms arelocated at the corners of the triangles: in each case there aretwo 0 atoms one above the other at a distance apart of 2.79Á.The H atoms are found between the two 0 layers; there areseveral theoretical possibilities as rcgards their precise position.(a) and (b) represent two possible configurations. In both caseseach H atom lies on the oblique line connecting an 0 atom inone layer to a neighbouring 0 atom in the other layer, at adistance of 0.96 Á from one of these 0 atoms (the O·H bondlength). These O-R bonds are indicated by the tail-ends of thearrows: a single arrow represents a bondwith an 0 atom in thelower layer, and a double arrow a bond with an 0 atom in theupper layer. The result of nuclear magnetic absorption analysisargues in favour of the configuration (a).

Appendix: Comparisonof nuclear magnetic resonance and para·magnetic resonance

In the introduetion to this article mention was made of therelation between the phenomena of nuclearmagnetic resonanceand paramagnetic resonance. It is perhaps useful to touch hereon some of the essential points of difference, some of whichhave already appeared in the foregoing pages.The measurement techniques used for studying the two

effects differ primarily in the wavelengths employed: para-magnetic-resonance investigations are performed at centi-metric wavelengths, and thus use klystrons, waveguldes andso on. Nuclear magnetic resonance is studied at wavelengthsof some tens of metres, which calls for ordinary radio valvesand transmission lines. This frequeney difference is directlyconnected with the fact that the magnetic moment of theeleetron, which is equal to ehj4.nm (Bohr magneton), is roughly1000 times greater than that of the proton or other nuclei.Nuclear moments according to equation (1) are principallygiven by ehj4nmp (nuclear magneton). As a result the twopossible states for an electron (with a spin parallel or anti-

1959/60, No. 10 NUCLEAR MAGNETIC RESONANCE 299

parallel to the external magnetic field) show an energy differ-ence LIE roughly 1000 times greater than that for a proton(see eq. (2». Accordingly the frequency ik at which nuclearmagnetic resonance occurs (see eq. (4» is given by:

eJk=g-4--B,.nmp

and the frequency of paramagnetic resonance Je (see eq. (5)in article 1» is given by:

eJe = ge -4 -- B.

·nm

Since, for practical reasons, the magnetic fields B for observingthe absorption due to electron spins and due to nuclear spinsare chosen at the same order of magnitude (0.1 to 1 Wb/m2),

and since the numerical factors g and ge in both formulae donot differ appreciably (ge ~ 2, and g lies between 0.1 and 10,as mentioned earlier), we see that the resonance frequenciesin the two methods differ by a factor of the order of 1000(proton mass mp = 1836 times electron mass m).Another practical and very important difference between

the two methods discussed concerns the sensitivity. Themeasurement of paramagnetic resonance is very much moresensitive than the measurement of nuclear magnetic resonance.This is again a direct consequence of the fact that for anelectron the two possible states with opposite spin orientationsshow an energy difference .dE about 1000 times greater thanfor a proton (confiningourselves now to protons). The relation-ship can be understood as follows. The difference between thenumbers of protons and electrons in the two states mentionedis proportional to .dE (see eq. (8), which is also valid forelectrons). The number of electron spins that can contributeto energy absorption from the alternating field is thereforeabout 1000 times greater than the number of proton spins,the total number per unit volume being the same. Moreoverthe energy quantum .dE absorbed from the alternating fieldupon each transition between the two states is also about1000 times greater (this has already appeared in the frequencydifference), so that the energy absorption - or the measuredsignal - other conditions being the same, is about lOG timesgreater for electrons than for protons.True, the detectors used for centimetric waves give a much

poorer signal-to-noise ratio than those for wavelengths of sometens of metres, and also the line width (to which the recordedintensity is inversely proportional) is several times larger inparametrie resonance than in nuclear magnetic resonance.Nevertheless the first method referred to remains far moresensitive than the other, which means that paramagnetic-resonance investigations can bc applied for very much smallerconcentrations of resonators.

It is precisely for this reason that such useful results havebeen achieved with paramagnetic resonance: the paramagneticcentres are usually present in only low concentrations, whereasin nuclear-magnetic-resonance studies the whole of the investi-gated substance enters into the measurement.This brings us to the last point of difference to be noted,

which concerns the information obtainable with the twomethods. Paramagnetic resonance provides information aboutthe immediate environment of a paramagnetic centre. Nuclearmagnetic resonance, on the other hand, gives information onthe structure of molecules or of crystals as a whole, and on theeffects of impurities (also non-paramagnetic impurities) onthat structure.

A recent further development of the techniques discussed isthe study of double resonance, where paramagnetic and nuclearmagnetic resonance are excited in a substanee simultaneously.This allows the nuclear magnetic resonance signal. to . beintensified, so that nuclei present in small concentrations arealso accessible to investigation 12). Moreover, the paramagnetic-resonance spectrum is influenced by the transitions betweenthe energy levels of different nuclear spin orientations 13). As aresult still more particulars can be learned about the propertiesof the solid state. There is no space here, however, to deal atgreater length with these .methods and their application.

12) A. W. Overhauser, Polarization of nuclei in metals, Phys.Rev. 91, 476, 1953. See also H. G. Beljers, L. van der Kintand J. S. van Wieringen, Overhauser effect in a free radical,Phys. Rev. 95, 1683, 1954.

13) This method is also referred to as "Endor' (electron nucleardouble resonance). See e.g. G. Feher, Electron spin reso-nance experiments on donors in silicon, Phys. Rev. 114,1219-1244, 1959 (No. 5).

Summary. Nuclear magnetic resonance gives rise to thespecific absorption of electromagnetic waves (best measurableat metre wavelengths) by certain atomic nuclei, particularlyhydrogen nuclei, when these are placed in a constant magneticfield. Since the resonance of a given nucleus is affected by thefields of neighbouring nuclei and electrons, the nuclear mag-netic absorption spectrum offersa variety of information on thesubstance containing the nuclei. In solids the effect appearsin a marked broadening of the resonance line; in liquids itappears in a splitting of the line into several componentsgrouped closely together. A concise explanation of the theoryof the phenomenon is followed by a description of two equip-ments used for recording the absorption spectra, one for liquidsand the other for solids. The essentially different requirementsof these two cases are dealt with at some length. In conclusionsome examples 'are discussed of the numerous uses to whichnuclear magnetic resonance has already been put, whichinclude the identification of compounds (analysis of organicliquids) and the structural analysis of molecules and crystals